Biomedical Engineering Reference
In-Depth Information
1.2
arbitrary rates
two rates
two patterns
1
0.8
0.6
0.4
0.2
0
0
0.25
0.5
0.75
delay [s]
Figure 18.12
Memory curves for spike patterns and firing rates. Dashed line: correlation of trained linear
readouts with the number of the templates used for generating the last input segment, and
the segments that had ended 250 ms, 500 ms, and 750 ms ago (for the inputs discussed in
Figure 18.11)
.
Solid lines: correlation of trained linear readouts with the firing rates for the
same time segments of length 250 ms that were used for the spike pattern classification task.
Thick solid line is for the case where the ideal input firing rates can assume just 2 values (30
or 60 Hz), whereas the thin solid line is for the case where arbitrary firing rates between 0
and 80 Hz are randomly chosen. In either case the actual average input rates for the 4 time
segments, which had to be recalled by the readouts, assumed of course a wider range.
planation is that the ensemble of liquid states reflecting preceding input spike trains
that all represented the same firing rate forms a much more complicated equivalence
class than liquid states resulting from jittered versions of a single spike pattern. This
problem is amplified by the fact that information about earlier firing rates is
over-
written
with a much more diverse set of input patterns in subsequent input segments
in the case of arbitrary Poisson inputs with randomly chosen rates. (The number of
concurrent input spike trains that represent a given firing rate is less relevant for these
memory curves; not shown.)
A theoretical analysis of memory retention in somewhat similar recurrent net-
works of sigmoidal neurons has been given in [11].
18.6.2
Kernel function of neural microcircuit models
It is well-known (see [22, 23, 25]) that the power of linear readouts can be boosted
by two types of preprocessing:
- computation of a large number of nonlinear combinations of input components
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